ESPM-EEP%202010%20Lecture%2011

ESPM-EEP%202010%20Lecture%2011 - ESPM 104/EEP 115 Fall...

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Unformatted text preview: ESPM 104/EEP 115 Fall 2010: Lecture 11 1. Gordon ­Schaefer Theory: exploitation of renewable resources contrasting maximum sustainable rent solutions (MSR) under sole ownership with bionomic solutions (Gordon’s principle: ( v∞ , x∞ ) ) under open access or common pool conditions. a. See Case 2000, p. 232 ­242. b. See Part II Harvesting Theory Notes c. See http://www.fao.org/DOCREP/003/W6914E/W6914E02.htm: d. See Gordon’s seminal paper at bSpace site e. See Schaefer’s seminal paper at bSpace site 2. Theory of sustainable harvesting under discounting: ∞ ⎡ ⎤ −δ t max ⎢Y ( v (t )) = ∫ e px (t ) − c v (t ) dt ⎥ v ∈[ 0 ,vmax ] ⎢ ⎥ 0 ⎣ ⎦ subject to dx = f ( x ) − xv and x (0) = x0 dt for f(x) a logistic ­like depensatory model. a. Equilibrium theory: Find equilibrium pair that maximizes Y(v(t)) i.e. the pair ( vδ , xδ ) ⇔ f ( xδ ) = vδ xδ such that ˆ ˆˆ Y ( vδ ) ≥ Y (v ) over all equilibrium pairs ( v, x ) with ˆ corresponding initial condition x (0 ) = x . b. Understand the relationship among solutions ( vMSY , xMSY ) , ( vMSR , xMSR ) , ( v∞ , x∞ ) and ( vδ , xδ ) and corresponding Yields c. Non ­equilibrium theory: how to approach ( vδ , xδ ) solution given that v ∈[ 0, vmax ] , assuming that vmax ≥ vδ . The solution is bang ­bang as discussed in class. d. See C.W. Clark 1976, 1985, and 2006 (The Worldwide Crisis in Fisheries, Cambridge University Press) for development of the theory ( ) ...
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This note was uploaded on 02/09/2011 for the course EEP 115 taught by Professor Waynem.getz during the Fall '10 term at University of California, Berkeley.

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